CANONICAL FORMALISM, FUNDAMENTAL EQUATION, AND GENERALIZED THERMOMECHANICS FOR IRREVERSIBLE FLUIDS WITH HEAT-TRANSFER

A Lagrangian with dissipative (e.g., Onsager's) potentials is construc ted for the field description of irreversible heat-conducting fluids, off local equilibrium. Extremum conditions of action yield Clebsch rep resentations of temperature, chemical potential, velocities, and gener alized momenta, including a thermal momentum introduced recently [R. L . Selinger and F. R. S. Whitham, Proc. R. Soc. London, Ser. A 302, 1 ( 1968); S. Sieniutycz and R. S. Berry, Phys. Rev. A 40, 348 (1989)]. Th e basic question asked is ''To what extent may irreversibility, repres ented by a given form of the entropy source, influence the analytical form of the conservation laws for the energy and momentum?'' Nother's energy for a fluid with heat flow is obtained, which leads to a fundam ental equation and extended Hamiltonian dynamics obeying the second la w of thermodynamics. While in the case of the Onsager potentials this energy coincides numerically with the classical energy E, it contains an extra term (vanishing along the path) still contributing to an irre versible evolution. Components of the energy-momentum tensor preserve all terms regarded standardly as ''irreversible'' (heat, tangential st resses, etc.) generalized to the case when thermodynamics includes the state gradients and the so-called thermal phase, which we introduce h ere. This variable, the Lagrange multiplier of the entropy generation balance, is crucial for consistent treatment of irreversible processes via an action formalism. We conclude with the hypothesis that embeddi ng the first and second laws in the context of the extremal behavior o f action under irreversible conditions may imply accretion of an addit ional term to the classical energy.